Question

express 2120 as the product of its prime

Answer 1

Start with the prime numbers 2,3,5,7,11,13

See if you can divide any of the above prime numbers into 2120 and get a whole number.

For example, you know 2120 can be divided by 5 since the number 2120 ends with a zero.
So 5 X 424= 2120.

Next look at the number 424. Can it be divided by one of the above prime numbers? Well it's an even number, so you know it's divisible by 2. So 2 X 212 =424.

So far we have 2 X 5 X 212 = 2120

However, 212 is also an even number, so it's divisible by 2. So 2 X 106 = 212

Now we have 2 X 2 X 5 X 106 = 2120

But wait, 106 is an even number so it's divisible by 2. So 2 X 53 =106

So now we have 2 X 2 X 2 X 5 X 53 = 2120

Is 53 a prime number? Well it's not an even number. So it's not divisible by 2, or any other even number.

If we sum the digits of 53, we get 5+3=8. We find 8 is not divisible by 3 or 9, so neither is the number 53.

We note the number 53 ends with a 3. So we know the number 53 is not divisible by 5. All numbers divisible by 5 end in a 5 or a 0.

So we just have to check to see if 53 is divisible by 7. Since 7 X 7 =49 and 7 X 8 = 56, we know 53 is not divisible by 7.

So 53 is a prime number.

So product of primes is 2 X 2 X 2 X 5 X 53 = 2120